Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system.

A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that this is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting liner flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.     

The exopolysaccharides produced by Streptococcus thermophilus Rs and Sts have the same repeating unit but differ in viscosity of their milk cultures

The polysaccharides produced by Streptococcus thermophilus Rs and Sts in skimmed milk consist of -Gal and -Rha in a molar ratio of 5:2. Linkage analysis and 1D/2D NMR (¹H and ¹³C) studies revealed that both polysaccharides have the same branched heptasaccharide repeating unit:

Full-size image

Remarkably, the two strains differ in their effects on the viscosity of stirred milk cultures. The milk culture of S. thermophilus Rs is non-ropy and affords 135 mg/L polysaccharide with an average molecular mass of 2.6×10³ kDa. In contrast, the milk culture of S. thermophilus Sts is ropy and produces 127 mg/L polysaccharide with an average molecular mass of 3.7×10³ kDa. Permeability measurements of non-stirred milk cultures of both strains suggest that both strains have a similar effect on the protein–polysaccharide network. Therefore, the only clear difference between both strains, which may cause the difference in ropiness of the milk cultures, is the difference in molecular mass of the polysaccharide.     

ＧＭ（１，Ｎ）模型对生物系统应用的研究

灰色系统理论的GM(1,N)模型已被广泛地用于生态,农业、林业等与生命现象有关的系统的分析和处理。但GM(1,N)本质上是一线性系统,在生态系统中,由于个体和种群的发展均受个体和种群间对有限资源竞争的限制,一般地说线性假设不能成立。本文对GM(1、N)在生态系统的适应性进行了探讨,提出丁系统线性度,系统非线性显著度的概念、定义和具体计算方法,并在此基础上建立了GM(1,N)模型的适用标准。将这一标准施用于计算机模拟的非线性程度不同的生态系统,结果说明本文所提出的系统表征的度量标准基本准确。另外,本文对GM(1,N)中的参数拟合略有改进,新方法在计算上有合理。省时等特点。     

A new algorithm for the identification of multiple input Wiener systems

Multiple-input Wiener systems consist of two or more linear dynamic elements, whose outputs are transformed by a multiple-input static non-linearity. Korenberg (1985) demonstrated that the linear elements of these systems can be estimated using either a first order input-ouput cross-covariance or a slice of the second, or higher, order input-output cross-covariance function. Korenberg's work used a multiple input LNL structure, in which the output of the static nonlinearity was then filtered by a linear dynamic system. In this paper we show that by restricting our study to the slightly simpler Wiener structure, it is possible to improve the linear subsystem estimates obtained from the measured cross-covariance functions. Three algorithms, which taken together can identify any multiple-input Wiener system, have been developed. We present the theory underlying these algorithms and detail their implementation. Simulation results are then presented which demonstrate that the algorithms are robust in the presence of output noise, and provide good estimates of the system dynamics under a wide set of conditions.     

Dominance, Pleiotropy and Metabolic Structure

It is a common observation that most mutants have similar dominance relations for all the characters they are known to affect. As a model of pleiotropic effects we investigate a branched pathway where the two outputs represent two characters whose variation is affected by changes in any of the genetically specified enzymes in the system. We consider the effects on the phenotype (fluxes or intermediate metabolites) of substitutions at one locus represented by enzyme activities of the two homozygotes (mutant and wild type) and that of the heterozygote. Dominance indices for the characters pleiotropically connected by the metabolic system are calculated. We show that if enzymes behave 'linearly,' (first order), that is if saturation and feedback inhibition or other nonlinearities are absent, all fluxes and pools have identical dominance relations. The presence of such nonlinearity, however, leads to differences in dominance between different characters and we define the conditions where such differences can be important.     

A simpler model of the human circadian pacemaker

Numerous studies have used the classic van der Pol oscillator, which contains a cubic nonlinearity, to model the effect of light on the human circadian pacemaker. Jewett and Kronauer demonstrated that Aschoff's rule could be incorporated into van der Pol type models and used a van der Pol type oscillator with higher order nonlinearities. Kronauer, Forger, and Jewett have proposed a model for light preprocessing, Process L, representing a biochemical process that converts a light signal into an effective drive on the circadian pacemaker. In the paper presented here, the authors use the classic van der Pol oscillator with Process L and Jewett and Kronauer's model of Aschoff's rule to model the human circadian pacemaker. This simpler cubic model predicts the results of a three-pulse human phase response curve experiment and a two-pulse amplitude reduction study with as much, or more, accuracy as the models of Jewett and Kronauer and Kronauer, Forger, and Jewett, which both employ a nonlinearity of degree 7. This suggests that this simpler cubic model should be considered as a potential alternative to other models of the human circadian system currently available.     

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model.     

Pendelluft flow in symmetric airway bifurcations.

We propose a mathematical model for pendelluft flow in a single airway bifurcation. The model is motivated by an apparatus used in an experimental study of the pendelluft by Ultman et al. (1988). We derive differential equations governing the fluid flow, which directly connect physiological parameters to the variables determining the pendelluft; this approach allows us to include nonlinearity in the model. If nonlinearity is neglected, our model is identical to the R-I-C circuits used by previous investigators. If nonlinearity is retained, we show that pendelluft can occur even in perfectly symmetric airway bifurcations. For the specific apparatus used in the experiments of High et al. (1991), we demonstrate that two qualitatively different pendelluft flows can occur in the system.     

On the choice of noise for the analysis of the peripheral auditory system

The cross-correlation between output and input of a system containing nonlinearities, when that system is stimulated with Gaussian white noise, is a good estimate of the linear properties of the system. In practice, however, when sequences of pseudonoise are used, great errors may be introduced in the estimate of the linear part depending on the properties of the noise. This consideration assumes special importance in the analysis of the linear properties of the peripheral auditory system, where the rectifying properties of the haircells constitute a second order nonlinearity. To explore this problem, a simple model has been designed, consisting of a second order nonlinearity without memory and sandwiched between two bandpass filters. Different types of pseudonoise are used as input whereupon it is shown that noise based on binary m-sequences, which is commonly used in noise generators, will yield totally incorrect information about this system. Somewhat better results are achieved with other types of noise. By using inverse-repeat sequences the results are greatly improved. Furthermore, certain anomalies obtained in the analysis of responses from single fibers in the auditory nerve are viewed in the light of the present results. The theoretical analysis of these anomalies reveals some information about the organization of the peripheral auditory system. For example, the possibility of the existence of a second bandpass filter in the auditory periphery seems to be excluded.     

Ion acoustic cnoidal waves in a dusty plasma with a critical dust density

The propagation of nonlinear periodic ion acoustic waves in a dusty plasma is considered for conditions in which the coefficient in the nonlinear equation that describes the quadratic nonlinearity of the medium is zero. An equation that accounts for the cubic nonlinearity of the system is derived, and its solution is found. The dependence of the phase velocity of a cnoidal wave on its amplitude and modulus is determined. In describing the effect of higher order nonlinearities on the properties of a dust ion acoustic wave, two coupled equations for the first- and second-order potentials are obtained. It is shown that the nonlinear ion flux generated by a cnoidal wave propagating in a medium with a cubic nonlinearity is proportional to the fourth power of the wave amplitude.     

Cooperative nonlinearities in auditory cortical neurons

Cortical receptive fields represent the signal preferences of sensory neurons. Receptive fields are thought to provide a representation of sensory experience from which the cerebral cortex may make interpretations. While it is essential to determine a neuron's receptive field, it remains unclear which features of the acoustic environment are specifically represented by neurons in the primary auditory cortex (AI). We characterized cat AI spectrotemporal receptive fields (STRFs) by finding both the spike-triggered average (STA) and stimulus dimensions that maximized the mutual information between response and stimulus. We derived a nonlinearity relating spiking to stimulus projection onto two maximally informative dimensions (MIDs). The STA was highly correlated with the first MID. Generally, the nonlinearity for the first MID was asymmetric and often monotonic in shape, while the second MID nonlinearity was symmetric and nonmonotonic. The joint nonlinearity for both MIDs revealed that most first and second MIDs were synergistic and thus should be considered conjointly. The difference between the nonlinearities suggests different possible roles for the MIDs in auditory processing.     

Hydraulic input impedance measurements in physical models of the arterial wall

A white noise method was used to measure the hydraulic input impedance and transmission characteristics in physical models of an arterial system made of single, unbranched latex tubes. The experimentally obtained impedance curves show a rise in modulus and a positive phase at high frequencies in the absence of wave reflections. Using the impedance moduli in the presence of wave reflections, wave velocity and attenuation were calculated. The influence of wall nonlinearity on hydraulic impedance was also examined. It is concluded that, in the model used neither wave reflections nor wall nonlinearity can account for the deviations of the experimental impedance curves from the theoretically predicted ones. Impedance moduli in the presence of reflections may be used to study transmission characteristics (wave velocity and attenuation) of the model.     

Modeling nonlinearity in dilution design microarray data

MOTIVATION: Dilution design (Mixed tissue RNA) has been utilized by some researchers to evaluate and assess the performance of multiple microarray platforms. Current microarray data analysis approaches assume that the quantified signal intensities are linearly related to the expression of the corresponding genes in the sample. However, there are sources of nonlinearity in microarray expression measurements. Such nonlinearity study in the expressions of the RNA mixtures provides a new way to analyze gene expression data, and we argue that the nonlinearity can reveal novel information for microarray data analysis. Therefore, we proposed a statistical model, called proportion model, which is based on the linear regression analysis. To approximately quantify the nonlinearity in the dilution design, a new calibration, beta ratio (BR) was derived from the proportion model. Furthermore, a new adjusted fold change (adj-FC) was proposed to predict the true FC without nonlinearity, in particular for large FC. RESULTS: We applied our method to one microarray dilution dataset. The experimental results indicated that, to some extent, there are global biases comparing with the linear assumption for the significant genes. Further analysis of those highly expressed genes with significant nonlinearity revealed some promising results, e.g. 'poison' effect was discovered for some genes in RNA mixtures. The adj-FCs of those genes with 'poison' effect, indicate that the nonlinearity can be also caused by the inherent feature of the genes besides signal noise and technical variation. Moreover, when percentage of overlapping genes (POG) was used as a cross-platform consistency measure, adj-FC outperformed simple fold change to show that Affymetrix and Illumina platforms are consistent. AVAILABILITY: The R codes which implements all described methods, and some Supplementary material, are freely available from http://www.utdallas.edu/~ying.liu/BetaRatio.htm     

White noise analysis of temporal properties in simple receptive fields of cat cortex

We studied the linear and nonlinear temporal response properties of simple cells in cat visual cortex by presenting at single positions in the receptive field an optimally oriented bar stimulus whose luminance was modulated in a random, binary fashion. By crosscorrelating a cell's response with the input it was possible to obtain the zeroth-, first-, and second-order Wiener kernels at each RF location. Simple cells showed pronounced nonlinear temporal properties as revealed by the presence of prominent second-order kernels. A more conventional type of response histogram was also calculated by time-locking a histogram on the occurrence of the desired stimulus in the random sequence. A comparison of the time course of this time-locked response with that of the kernel prediction indicated that nonlinear temporal effects of order higher than two are unimportant. The temporal properties of simple cells were well represented by a cascade model composed of a linear filter followed by a static nonlinearity. These modelling results suggested that for simple cells, the nonlinearity occurs late and probably is a soft threshold associated with the spike generating mechanism of the cortical cell itself. This result is surprising in view of the known threshold nonlinearities in preceding lateral geniculate and retinal neurons. It suggests that geniculocortical connectivity cancels the earlier nonlinearities to create a highly linear representation inside cortical simple cells.This work comprises a portion of a PhD thesis submitted by the first author. This study was supported in part by NIH Grant EY04630 and EY06679 to R.C.E., and EY01319 (Core Grant) to the Center for Visual Science     

Frequency tuning in the electroreceptive periphery.

Our studies are concerned with the frequency tuning that is provided by the electrical resonance of tuberous electroreceptors. Frequency selectivity had previously been measured in the electroreceptor's afferent fibers, and resonant conductances in the electroreceptor cell membrane had been implicated in producing the selectivity. With transdermal application of sinusoidal current, we measured the frequency dependence of the impedance of small areas of the electroreceptor/skin structure of the weakly electric fish Sternopygus and Eigenmannia, and used our data to make a quantitative linear model of the structure. The qualitative form of the model was proposed by Bennett (1). The quantitative model allows us to estimate the frequency selectivity of the voltage across the innervated membrane of the electroreceptor cells. The frequency selectivity of electroreceptor cell voltage derived from our data are as sharp as the neural selectivity at frequencies close to the most sensitive frequency. Many of our measurements supported the linear system model. However, spontaneous electroreceptor voltage oscillations were detected in some of our specimens, suggesting that the electroreceptors can operate in a regime of active nonlinearity. A simple explanation for the observed oscillations is that they arise when damping in the electroreceptor cell's resonant membrane is negative for a limited span of membrane voltage surrounding the resting voltage. The response of oscillating units to sinusoidal current was compatible with this explanation. We report experimental observations bearing on the consequences of active nonlinearity for the frequency tuning of a resonant system.     

Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener–Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal). The static nonlinearity, which can be viewed as a measure of the probability of action potential firing as a function of the PDM output values, is computed as the locus of points of the latter that correspond to output action potentials. The performance of the model is assessed by computing receiver operating characteristic (ROC) curves, akin to the ones used in decision theory and quantified by computing the area under the ROC curve. Three PDMs are revealed by the analysis. The first PDM exhibits a high-pass characteristic, illustrating the importance of the velocity of slit displacement in the generation of action potentials at the mechanoreceptor output, while the second and third PDMs exhibit band-pass and low-pass characteristics, respectively. The corresponding three-input nonlinearity exhibits asymmetric behavior with respect to its arguments, suggesting directional dependence of the mechanoreceptor response on the mechanical stimulation and the PDM outputs, in agreement to our findings from a previous study (Ann Biomed Eng 27:391–402, 1999). Differences between the Type A and B neurons are observed in the zeroth-order Volterra kernels (related to the average firing), as well as in the magnitudes of the second and third PDMs that perform band-pass and low-pass processing of the input signal, respectively.     

Constant and variable stiffness and damping of the leg joints in human hopping

The present study deals with the stiffness and damping profiles of the leg joints during the ground-contact phase of hopping. A two-dimensional (sagittal plane) jumping model, consisting of four linked rigid segments and including the paired feet, shanks, thighs, and the head-arms-trunk segment, was developed. The segments were interconnected by damped torsional springs, representing the action of the muscles, tendons and ligaments across the joint and of the other joint tissues. A regressive function was used to express stiffness and damping, and included second-order dependence on angle and first-order dependence on angular velocity. By eliminating redundancies in the numerical solution using multicollinearity diagnostic algorithms, the model results revealed that the correct and sufficient nonlinearity for the joint stiffness is of the first order. Damping was found negligible. The stiffness profiles obtained were bell-shaped with a maximum near midstance and nonzero edge values. In predicting the joint moments, the obtained variable joint stiffnesses provided a closer agreement compared to a constant stiffness model. The maximal stiffness was found to be in linear correlation with the initial stiffness in each joint, providing support to the of muscles' preactivation strategy during the flight phase of hopping. All stiffnesses increased with increasing hopping frequency. The model presented provides an effective tool for future designing of artificial legs and robots and for the development of more accurate control strategies.     

A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade

This paper describes a general nonlinear dynamical model for neural system identification. It describes an algorithm for fitting a simple form of the model to spike train data, and reports on this algorithm's performance in identifying the structure and parameters of simulated neurons. The central element of the model is a Wiener-Bose dynamic nonlinearity that ensures that the model is able to approximate the behaviour of an arbitrary nonlinear dynamical system. Nonlinearities associated with spike generation and transmission are treated by placing the Wiener-Bose system in cascade with pulse frequency modulators and demodulators, and the static nonlinearity at the output of the Wiener-Bose system is decomposed into a rectifier and a multinomial. This simplifies the model without reducing its generality for neuronal system identification. Model elements can be characterised using standard methods of dynamical systems analysis, and the model has a simple form that can be implemented and simulated efficiently. This model bears a structural resemblance to real neurons; it may be regarded as a connectionist neuron that has been generalized in a realistic way to enable it to mimic the behaviour of an arbitrary nonlinear system, or conversely as a general nonlinear model that has been constrained to make it easy to fit to spike train data. Tests with simulated data show that the identification algorithm can accurately estimate the structure and parameters of neuron-like nonlinear dynamical systems using data sets containing only a few hundred spikes.     

Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63-72, Lai et al., 1991, J. Biomech. Eng., 113, pp. 245-258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576-586; Curnier et al., 1995, J. Elasticity, 37, pp. 1-38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.